Heisenberg’s Uncertainty Principle. Why, exactly, can you not know both the velocity and position of a particle?
In: 146
**TLDR**
Particles are small and small things behave more like waves than large objects. Waves are spread out and so they don’t exist in a precise location, and if they aren’t spread out, then they are less like a wave and move with ambiguous speed.
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**More technical:**
As the size of an object decreases (the limit of this we can consider a “particle”), the wavelike properties of that object become more important.
The wavefunction of a particle tells you where a particle may be with a certain probability, and the wavefunction is a wave.
The least useful wavefunction in determining where a particle may be would be a sine/cosine function that spreads out in all of space with complete uniformity.
Imagine this wave extending throughout all of space. Ok, so the uncertainty in position of this wave is infinity. The particle could be in Hawaii, or Alpha Centauri, or whereever with equal probability.
However, in this case we have a perfect wave which means we have a perfect wavelength (the distance between peaks/crests of the wave)
https://www.nasa.gov/sites/default/files/styles/side_image/public/thumbnails/image/edu_wavelength_large.png?itok=zSOpfUKm
The wavelength is related in an exact equation to the momentum which gives you the velocity. So if we know the wavelength with high precision, we know the velocity with high precision.
The inverse is if our spread out wave is now condensed into one little crest.
In this case, we have a great understanding of where the wave is (its just in the small region where the crest is), but now since it looks less uniform as a wave, its wavelength and thus velocity is more poorly defined.
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